{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UUFXZNFVH3XIXHH5V3GBVD3B7H","short_pith_number":"pith:UUFXZNFV","canonical_record":{"source":{"id":"1201.2193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-10T21:36:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7b4d5f6b657041f0598a8be4f0f551c8797b9eef9e43997edfaa4a34ec136a0f","abstract_canon_sha256":"113bff99a571e2d70460d29bcad98ff57ed503bff5442760423e5c5e2bac1b4e"},"schema_version":"1.0"},"canonical_sha256":"a50b7cb4b53eee8b9cfdaecc1a8f61f9f2dee176b7e9b649a6593ea5bf994b37","source":{"kind":"arxiv","id":"1201.2193","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2193","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2193v2","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2193","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"UUFXZNFVH3XI","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UUFXZNFVH3XIXHH5","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UUFXZNFV","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UUFXZNFVH3XIXHH5V3GBVD3B7H","target":"record","payload":{"canonical_record":{"source":{"id":"1201.2193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-10T21:36:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7b4d5f6b657041f0598a8be4f0f551c8797b9eef9e43997edfaa4a34ec136a0f","abstract_canon_sha256":"113bff99a571e2d70460d29bcad98ff57ed503bff5442760423e5c5e2bac1b4e"},"schema_version":"1.0"},"canonical_sha256":"a50b7cb4b53eee8b9cfdaecc1a8f61f9f2dee176b7e9b649a6593ea5bf994b37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:00.559716Z","signature_b64":"8T3BjuKE+m7pU2BKJyDY+W2I+SF3kU189q4z8JUtw5yDMA/dr2cUzOO97QZelpNmu4zoqE/tif61RTD+qLKfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a50b7cb4b53eee8b9cfdaecc1a8f61f9f2dee176b7e9b649a6593ea5bf994b37","last_reissued_at":"2026-05-18T02:32:00.559085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:00.559085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.2193","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caz5ZBsbGXQvuzm1/mdwynKwUh+iFOlsFXPyT2emyYSPgoAIWb+FCAcE7TVaA3NjeIY+K7wRYPzCgk6ev5ToBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T04:26:14.989050Z"},"content_sha256":"77bf4e71a1baadc20a09b92f54097f7108a3ac704def1ef7859eafec32b28d8c","schema_version":"1.0","event_id":"sha256:77bf4e71a1baadc20a09b92f54097f7108a3ac704def1ef7859eafec32b28d8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UUFXZNFVH3XIXHH5V3GBVD3B7H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arrangements of Spheres and Projective Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Priyavrat Deshpande","submitted_at":"2012-01-10T21:36:20Z","abstract_excerpt":"We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of intersections. We also associate a topological space: the complement of the union of tangent bundles of these subspheres in the tangent bundle of the ambient sphere. We call this space the tangent bundle complement. As in the case of hyperplane arrangements the aim of this new notion is to understand the interaction between the combinatorics of the intersections an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2193","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avfFGWz/uf2Vkj2g3V7PNcqXEW+nLz1DiUOfnjWWN72UfFEDig0JVARNuj4oSB1VpdWv9YaXvciNk+iGyd7HAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T04:26:14.989399Z"},"content_sha256":"b23d5abe7a52b2d74c0bcab84ca81b6a13f596c200cf4646f1373ac787daeb29","schema_version":"1.0","event_id":"sha256:b23d5abe7a52b2d74c0bcab84ca81b6a13f596c200cf4646f1373ac787daeb29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUFXZNFVH3XIXHH5V3GBVD3B7H/bundle.json","state_url":"https://pith.science/pith/UUFXZNFVH3XIXHH5V3GBVD3B7H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUFXZNFVH3XIXHH5V3GBVD3B7H/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-04T04:26:14Z","links":{"resolver":"https://pith.science/pith/UUFXZNFVH3XIXHH5V3GBVD3B7H","bundle":"https://pith.science/pith/UUFXZNFVH3XIXHH5V3GBVD3B7H/bundle.json","state":"https://pith.science/pith/UUFXZNFVH3XIXHH5V3GBVD3B7H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUFXZNFVH3XIXHH5V3GBVD3B7H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UUFXZNFVH3XIXHH5V3GBVD3B7H","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"113bff99a571e2d70460d29bcad98ff57ed503bff5442760423e5c5e2bac1b4e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-10T21:36:20Z","title_canon_sha256":"7b4d5f6b657041f0598a8be4f0f551c8797b9eef9e43997edfaa4a34ec136a0f"},"schema_version":"1.0","source":{"id":"1201.2193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2193","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2193v2","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2193","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"UUFXZNFVH3XI","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UUFXZNFVH3XIXHH5","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UUFXZNFV","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:b23d5abe7a52b2d74c0bcab84ca81b6a13f596c200cf4646f1373ac787daeb29","target":"graph","created_at":"2026-05-18T02:32:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of intersections. We also associate a topological space: the complement of the union of tangent bundles of these subspheres in the tangent bundle of the ambient sphere. We call this space the tangent bundle complement. As in the case of hyperplane arrangements the aim of this new notion is to understand the interaction between the combinatorics of the intersections an","authors_text":"Priyavrat Deshpande","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-10T21:36:20Z","title":"Arrangements of Spheres and Projective Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2193","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:77bf4e71a1baadc20a09b92f54097f7108a3ac704def1ef7859eafec32b28d8c","target":"record","created_at":"2026-05-18T02:32:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"113bff99a571e2d70460d29bcad98ff57ed503bff5442760423e5c5e2bac1b4e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-10T21:36:20Z","title_canon_sha256":"7b4d5f6b657041f0598a8be4f0f551c8797b9eef9e43997edfaa4a34ec136a0f"},"schema_version":"1.0","source":{"id":"1201.2193","kind":"arxiv","version":2}},"canonical_sha256":"a50b7cb4b53eee8b9cfdaecc1a8f61f9f2dee176b7e9b649a6593ea5bf994b37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a50b7cb4b53eee8b9cfdaecc1a8f61f9f2dee176b7e9b649a6593ea5bf994b37","first_computed_at":"2026-05-18T02:32:00.559085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:00.559085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8T3BjuKE+m7pU2BKJyDY+W2I+SF3kU189q4z8JUtw5yDMA/dr2cUzOO97QZelpNmu4zoqE/tif61RTD+qLKfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:00.559716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77bf4e71a1baadc20a09b92f54097f7108a3ac704def1ef7859eafec32b28d8c","sha256:b23d5abe7a52b2d74c0bcab84ca81b6a13f596c200cf4646f1373ac787daeb29"],"state_sha256":"c205db39e9b09438e30320376e9d33d2a1ee9f0e387814759e8c08086af200b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pKwkexYSOvoWGVwq0Sg13yiLKRFs/uq6e5dRAx7fLXogf503AdEZYLrkDDj48GLFfGpl5cUKxc3iJJkJhetiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T04:26:14.991357Z","bundle_sha256":"e4557963f9e3ec08185fb9be814733eceb5cd1eb2be5f58ec052aa9b940b81ec"}}